Infinite Buffer Capacity Research Articles

Transient analysis of a switched Poisson arrival queue under overload control

This paper studies the transient behavior of a Switched Poisson Arrival Queue (SPAQ) under overload control. The queue has infinite buffer capacity with an exponential server. A switched Poisson process is used to represent an aggregated voice/data packet arrival process in integrated services networks. By overload control, we mean to properly adapt the arrival process once the buffer contents exceed a designated level. The probability distribution of queue length as a function of time is obtained. The temporal effect of the overload control is measured in two forms. While in overload, we measure the amount of time for the queue to fall into an underload period. While in underload, we measure the amount of time for the queue to rise to an overload period. a proper design of the control will not only reduce the fall time but also increase the rise time, to protect high priority and time constrained services. Our study provides important information to overload control design on packet switching networks. We also explore the transient queueing behavior as affected by time stochastic properties of the underlying two-state Markov chain for the arrival process.

Transient analysis of multi-server queues with Markov-modulated Poisson arrivals and overload control

This paper studies the transient behavior of a Markov-molulated Poisson arrival queue under overload control. The queue has finite or infinite buffer capacity with multiple exponential servers. A Markov-modulated Poisson process is used to represent an aggregated voice or video packet arrival process in integrated service networks. By overload control, we mean to properly adapt the arrival process once the buffer contents exceed a designated level. The probability distribution of queue length as a function of time is obtained. The temporal effect of the overload control is measured in two forms. While in overload, we measure the amount of time for the queue to fall into underload. While in underload, we measure the amount of time for the queue to rise to overload. A proper design of the control will not only reduce the fall time but also increase the rise time. We also explore the transient queueing behavior as affected by time stochastic properties of the underlying Markov chain for the arrival process.

Performance analysis of a queuing system with facilities requiring post-processing

This paper considers a queuing system in which a fixed number of identical facilities (servers) are employed one at a time for providing individual customer service at the single service station with unit capacity and each facility undergoes a post-processing after serving its own customer. Customers arrive in a Poisson process, and the customer service time and the facility post-processing time distributions are all exponential. For the queuing system, two different cases, the loss system (finite buffer capacity) and the delay system (infinite buffer capacity), will be analyzed separately to exploit their approximate computation algorithms for the associated long-run system state distributions. The algorithms are then tested for efficiency and effectiveness with various numerical problems.

Performance analysis of virtual circuit connections for bursty data sources in ATM networks

ATM is a packet-like transmission mode that has been proposed for BISDN. It is characterized by an asynchronous slotted transmission mechanism that provides a high bandwidth, low delay connection-oriented transport service to the end user. In this paper, we provide an analytical approach for determining the performance of a virtual circuit connection for data transmission in a high-speed ATM network with finite buffers at the network nodes. The analysis assumes that the network operates using thebest effort delivery strategy and that the end-to-end virtual circuit is responsible for guaranteeing the integrity of the connection. Since the normal Markovian assumptions do not apply, a concise exact solution is impossible to obtain. This provides motivation for developing approximate techniques such as those found in Whitt's QNA paper that allow us to use general distributions for the traffic streams and service times. However, even these techniques assume infinite buffer capacities and hence cannot model buffer overflow. We have therefore developed a hybrid model that allows us to incorporate finite buffers at the nodes. This enables us to study the effect on the performance of both link errors and buffer overflow in conjunction with an end-to-end packet loss recovery scheme.

Obtaining derivatives of stationary queue length probabilities through the matrix-geometric solution method

In this paper, we show that using the matrix-geometric solution method we can express the derivatives of the stationary queue length probabilities of the M/ PH/1/ K queue or the M/ PH/1/(∞, K) multiclass queue in terms of the stationary queue length probabilities of the M/ PH/1 queues with infinite buffer capacity. The results can be used in the optimization of networks consisting of nodes with finite buffers.

Performance modelling of a cell multiplexer for bursty ATM traffic

Abstract A cell multiplexer handling bursty asynchronous transfer mode (ATM) traffic is analysed by simulation to evaluate the relationship between the cell delay and the input traffic parameters. The traffic on an input line of the multiplexer is characterized by three parameters: the average burst length (L a) expressed in terms of the number of cells; the peak bit rate (R p) in bits−1; and the average inter-arrival time between two bursts (IATa) in seconds. The performance measures are the average and the 99% values of the queueing delay of a cell. The cell multiplexer is assumed to have an infinite buffer capacity, which means there are no cell losses due to buffer overflow. Besides the particular traffic configuration in which the inputs have the same traffic type (identical inputs or homogeneous traffic configuration), the study addresses some other traffic configurations in which the inputs do not have the same traffic type (non-identical inputs or inhomogeneous traffic configuration).

A heavy traffic analysis for semi-open networks

Systems arising in the performance modelling of data communication networks and manufacturing job shops have flow constraints that occur in neither purely open nor purely closed queueing network models. In this article, we analyze a class of queueing networks that are semi-open. One node is identified as the feeder node, like a CPU or a schedular. It receives all the external arrivals to the system, and has an infinite buffer capacity. Jobs then leave to enter a larger flow controlled network. When the number in this part of the system equals K, the server for the feeder queue shuts down, and no more customers are admitted into this controlled network. Semi-open networks have been analyzed exactly for one or two nodes in the controlled subnetwork by Konheim and Reiser [A.G. Konheim, M. Reiser, J. ACM vol. 23, no. 2, 328–341; and SIAM J. Computing vol. 7, no. 2 (1978) 210–219], and asymptotically for a one node subnetwork by Kogan and Pukhalskii [Y.A. Kogan, A.A. Pukhalskii, in Performance '84, ed. E. Gelenbe (Elsevier, 1984) pp. 549–558]. The latter set of authors analyzed this system by obtaining a heavy traffic limit for the feeder queue, and the subnetwork had the limiting distribution of the M/M/1/K queue. In this article, we generalize the results of Kogan and Pukhalskii to the case of the subnetwork being a flow controlled Jackson network with an arbitrary number of nodes. To obtain the heavy traffic limit, we need to compute the variance for the effective service times of the feeder queue. This variance can be solved in terms of covariances for the departure process of the flow controlled network with a Poisson source, and the event that the network is in some state. In turn, we show that these covariances can be computed by solving a finite set of linear equations. We derive these equations by using Kronecker products to decompose the Markov generator for the queueing network into right and left shift operators.

An optimal policy for competitive processing of high‐ and low‐priority arrivals

AbstractWe consider two mutually independent traffic streams whose arrivals are stored in an infinite capacity buffer. The two arrival traffics are modelled by renewal processes and are competing for service by a single processor, where one of the processes requires a strict upper bound on the total delay per arrival. It is assumed that the processing per arrival, for both processes, is a constant; the value of this constant is different for each of the two traffic streams.Given the above model, we consider policies that operate in a non‐interruptive mode. We first find the optimal scheduling policy, which attains throughput one and minimizes the expected delays of both traffic streams. The delays induced by the latter policy are analysed via a methodology based on the regenerative theorem. The theoretical results are supported by numerical examples.

Optimal routing to parallel heterogeneous servers-small arrival rates

Consider a set of k(>or=2) heterogeneous and exponential servers that operate in parallel. Customers arrive into a single infinite capacity buffer according to a Poisson process, and are routed to available servers in accordance with some routing policy. It is shown that for arrival rates in some possible interval (0, lambda /sub 0/), ever routing policy which minimizes the long-run expected holding cost is contained in the set of routing policies that minimize the expected flow time for a system with fixed initial population and no new arrivals. >

Quality control of an unreliable flexible manufacturing system with scrapping and infinite buffer capacity

Manufacturing multiple part types on a flexible manufacturing system (FMS) is increasingly becoming a rule rather than an exception. In such systems, attention has been drawn to the application of zero-defect technologies. However, in practice, this goal has remained elusive and costly. As a result, even though FMSs may be more reliable, producing fewer defective parts, system complexity and more stringent quality standards are rendering quality control in FMSs potentially useful. The goals of this article are threefold. First, we introduce a procedure for measuring and managing the in-process quality control of an FMS, which is described by an Open Queueing Network (OQN), bridging thereby a gap between queueing theory and quality control. Second, by focusing attention on the potential unreliabilities of FMSs, we provide some managerial insights regarding the role, position, and distribution of the quality control effort in an FMS. Finally, we stress the intricate relations between an FMS's operating characteristics and the manufactured quality and its control. Using numerical analyses, we draw some inferences regarding the design of such FMSs when both quality and quantity issues in the FMSs are considered. These simultaneous considerations of quantity and quality flows in an FMS have not been previously considered in the study of FMSs.

Analytic models of cyclic service systems and their application to token-passing local networks

Using the framework of cyclic-service systems with a single server, two different token-passing models are investigated. The first model is approximate, obtaining the free-tokens cycle-time distribution on an asymmetric system with infinite capacity buffers and single-token operation. The second model is exact, yielding the cycle-time distribution of the free token on an asymmetric system with unit-capacity buffers, and single-token operation. The latter result is verified using known results for symmetric, unit-capacity buffer systems. To demonstrate the positive effects of buffering, a small variation of the unit-capacity buffering scheme is introduced. Computational results include performance measures such as throughput, utilization, loss probabilities, mean cycle times, cycle-time distributions, and a comparison of two buffering schemes.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Bounds for Queue Lengths in a Contention Packet Broadcast System

A finite number of users communicating through a broadcast channel is considered. Each user has a buffer of infinite capacity, and a user randomly accesses the channel (ALOHA-type protocol). Moreover, only one packet per user might be sent in an access time. Both symmetric and asymmetric models are considered; that is, we assume either indistinguishable or distinguishable users. An exact analysis of the queue lengths in that type of system is not now available, and therefore, based on some algebraic studies, we shall present some lower and some upper bounds for the average queue lengths. These bounds are quite tight for a small number of users and acceptable for a wide range of input parameters in the symmetric case. In the asymmetric case the bounds are acceptable only for light input traffic and a small number of users.

A model to approximate transient performance of the flowshop

SUMMARY Transient performance of the flowshop is approximated using a model which is based on the assumption that operation start and finish times are related by the multivariate normal distribution. Start times are defined by evaluating the maximum of the finishing times which determine the epoch at which an operation can begin. Fundamental relationships among the correlations of start and finishing times are derived and used in several computational procedures to estimate start times. Examples which demonstrate application of the approach to flowshops with finite and infinite buffer capacities are given. Applications of the approach to more complex queueing networks and assembly systems are described.

Two competing queues with linear costs and geometric service requirements: the μc-rule is often optimal

A discrete-time model is presented for a system of two queues competing for the service attention of a single server with infinite buffer capacity. The service requirements are geometrically distributed and independent from customer to customer as well as from the arrivals. The allocation of service attention is governed by feedback policies which are based on past decisions and buffer content histories. The cost of operation per unit time is a linear function of the queue sizes. Under the model assumptions, a fixed prioritization scheme, known as the μc-rule, is shown to be optimal for the expected long-run average criterion and for the expected discounted criterion, over both finite and infinite horizons. Two different approaches are proposed for solving these problems. One is based on the dynamic programming methodology for Markov decision processes, and assumes the arrivals to be i.i.d. The other is valid under no additional assumption on the arrival stream and uses direct comparison arguments. In both cases, the sample path properties of the adopted state-space model are exploited.

Two competing queues with linear costs and geometric service requirements: the μc-rule is often optimal

A discrete-time model is presented for a system of two queues competing for the service attention of a single server with infinite buffer capacity. The service requirements are geometrically distributed and independent from customer to customer as well as from the arrivals. The allocation of service attention is governed by feedback policies which are based on past decisions and buffer content histories. The cost of operation per unit time is a linear function of the queue sizes. Under the model assumptions, a fixed prioritization scheme, known as the μc-rule, is shown to be optimal for the expected long-run average criterion and for the expected discounted criterion, over both finite and infinite horizons. Two different approaches are proposed for solving these problems. One is based on the dynamic programming methodology for Markov decision processes, and assumes the arrivals to be i.i.d. The other is valid under no additional assumption on the arrival stream and uses direct comparison arguments. In both cases, the sample path properties of the adopted state-space model are exploited.

Queueing analysis of buffered slotted multiple access protocols

Much of the literature on the performance evaluation of multiple access protocols has assumed a buffer capacity of one unit. This assumption is not realistic. In practice the buffer capacities used are larger than one unit in order to reduce the probability of packet rejection. This is more crucial for multiple access protocols, which allow moderate to high values of the expected throughput (URN, Random TDMA etc.). In this paper, a model appropriate for the analysis of buffered slotted multiple access schemes is proposed. The method can be applied to several multiple access protocols such as the URN protocol, the ALOHA protocol, Random TDMA etc. The cases of infinite and finite buffer capacity are examined separately but under the same basic assumptions. The analysis is based on the assumption that each user process can be modelled as an M/G/1 queueing system. The proposed method requires a small amount of computation and is characterized by a high speed, a fact that simplifies the buffer's design as well. The solution obtained is extremely accurate and exhibits excellent agreement with simulation results, which corroborate the accuracy of the model. The special case when the buffer capacity is equal to 1 is examined. In that case, the present approach also allows for computation of the packet delay distribution.

Token ring local area networks: A comparison of experimental and theoretical performance

Many existing performance models for local area networks are based on the assumptions of random traffic patterns and infinite buffer capacity. All real network implementations violate the infinite capacity assumption, while an increasingly popular class of local area network applications violates the randomness assumption. This paper describes the experimental measurements of the characteristics of a commercially available token ring network. It is shown that the violation of both assumptions invalidates model predictions, and that the utility of all access control mechanisms for such applications must be re-evaluated. Finally, it is shown that congestion is a very real problem even in small “simple” local area networks. Schemes for controlling interface congestion may require rather novel approaches to the problem.

Two competing queues with linear costs: the μc-rule is often optimal

A state-space model is presented for a queueing system where two classes of customer compete in discrete-time for the service attention of a single server with infinite buffer capacity. The arrivals are modelled by an independent identically distributed random sequence of a general type while the service completions are generated by independent Bernoulli streams; the allocation of service attention is governed by feedback policies which are based on past decisions and buffer content histories. The cost of operation per unit time is a linear function of the queue sizes. Under the model assumptions, a fixed prioritization scheme, known as the μc -rule, is shown to be optimal when the expected long-run average criterion and the expected discounted criterion, over both finite and infinite horizons, are used. This static prioritization of the two classes of customers is done solely on the basis of service and cost parameters. The analysis is based on the dynamic programming methodology for Markov decision processes and takes advantage of the sample-path properties of the adopted state-space model.

Analysis, stability, and optimization of slotted ALOHA with a finite number of buffered users

This paper analyzes the slotted ALOHA multiple access scheme for satellite channels with a finite number of users, each having a buffer of infinite capacity. The basic contribution of the paper is the introduction of an improved 2-Markov chain model that permits analysis of this heretofore unsolved problem. Finding an optimal value for the retransmission probability, p that minimizes the total average packet delay and at the same time ensures stability is also discussed.

Behavior of Tandem Buffers with Geometric Input and Markovian Output

A discrete-time system of infinite-capacity buffers in tandem is studied. The input process to the first buffer consists of individual arrivals characterized by a geometric distribution of the time between arrivals; and the probability that the output channel of each buffer, except the last, is transmitting at any epoch depends only on the number of digits in the buffer at that epoch. The transmitting state of the last buffer may depend more generally on the history of that buffer. The analysis shows that in equilibrium, the input processes to the subsequent buffers in the system are geometric with the same parameter as the input process to the first buffer. Therefore, each buffer in the system can be analyzed separately. Furthermore, the equilibrium state probabilities for a given buffer at a given epoch are independent of those for any other buffer in the system at the same epoch.